Question 1164935
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In factored form, a quadratic equation is of the form<br>
{{{y = a(x-p)(x-q)}}}<br>
If x is equal to either p or q, then the value of y is zero, because one of the factors (x-p) or (x-q) is zero.<br>
The values p and q -- that make the y value zero -- are called the roots of the equation.<br>
In a graph, that means the graph crosses the x-axis at x=p and at x=q.<br>
In this example, the graph crosses the x-axis at x=-3 and at x=-4.  So the quadratic equation is of the form<br>
{{{y = a(x-(-3))(x-(-4))}}}<br>
or<br>
{{{y = a(x+3)(x+4)}}}<br>
What is left to do is to determine the value of the coefficient a.<br>
To do that, use any point on the graph other than an x-intercept.<br>
In this example, it looks as if y=2 when x=-2.  So plug those coordinates into the formula and solve for a.<br>
{{{2 = a((-2)+3)((-2)+4)}}}
{{{2 = a(1)(2)}}}
{{{a = 1}}}<br>
So the equation for the graph is<br>
{{{y = 1(x+3)(x+4)}}}<br>
or just<br>
{{{y = (x+3)(x+4)}}}<br>